He needs voters to believe this isn’t part of a pattern, given White’s claim that the relationship began at the same time — in the late 1990s, when Cain was head of the National Restaurant Association — that other women were complaining of sexual harassment by Cain.

He needs voters to believe it’s possible Sharon Bialek was so publicity- and money-hungry a few weeks earlier that she made up her public, on-camera allegation that Cain tried to grab her genitals and then forced her head toward his crotch. He says it never happened and that he’s never met her. That would mean that a Chicago talk-radio host who saw the two together at a tea party rally in Illinois this year is also lying. Cain’s campaign circulated stories about her financial woes and her attorney’s Democratic ties, an unmistakable suggestion that Bialek, a registered Republican, was acting for financial or political gain.

He needs voters to believe that Karen Kraushaar is a liar, too — that she was so sensitive or so vindictive that she marched into the NRA’s human resources department in 1999 to file a bogus sexual harassment complaint against Cain, then her boss. Cain says the only thing he recalls ever saying to her was that she was the same height as his wife.

He needs voters to believe it’s possible the association’s legal counsel reviewed the matter at the time, concluded it was baseless — and then coughed up about $45,000 in a termination settlement that forbade her from ever disparaging Cain or other NRA executives.

He also needs voters to believe it’s possible that POLITICO, NBC, and then The New York Times, The Washington Post, The Associated Press, The Wall Street Journal and many other media outlets heard about her complaint — and decided to conspire against the GOP front-runner by running stories about it.

It’s possible, his attorney has claimed, that Kraushaar did it for partisan reasons because she works in a nonpartisan, career civil service position in the government, presently run by a Democrat, despite her registration as a Republican. Voters would have to ignore the fact that Kraushaar previously worked in a similar career capacity for President George W. Bush, a Republican.